Unstable BP-operations and typical formal groups Original Research Article

We prove that the functor taking a Z(p)-algebra R to the set of homomorphisms of p-typical formal group laws over R is represented by the ring of additive unstable BP-cooperations. This is analogous to a result of Landweber concerning stable BP-cooperations and strict isomorphisms of formal groups. Using this point of view we are able to reproduce the formulae of Boardman-Johnson-Wilson describing the additional structure in QBP*BP2*. Finally we discuss the set of multiplicative additive unstable BP-operations and give a characterisation in terms of homomorphisms of formal group laws.